Single-particle relaxation time of one-dimensional electron gases

Abstract

The single-particle relaxation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}$ for the disordered interacting quasi-one-dimensional electron gas is calculated within a one-subband model. For interface-roughness scattering and alloy-disorder scattering, we find that the ratio between the transport relaxation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}$ and ${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}$, if they are calculated in the lowest-order Born approximation, is given by ${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}$/${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}$=1/2. For charged-impurity scattering we derive ${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}$/${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}$\ensuremath{\gg}1 for ${\mathit{E}}_{\mathit{F}}$${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}$\ensuremath{\gg}1, where ${\mathit{E}}_{\mathit{F}}$ is the Fermi energy. Multiple-scattering effects calculated with the self-consistent Born approximation are also discussed. The density of states versus energy in the presence of disorder is calculated. We present analytical results, and recent experimental and theoretical results are discussed.